Physics Homework Help

Question

Before the advent of solid-state electronics, vacuum tubes were widely used in radios and other devices. A simple type of vacuum tube known as a diode consists essentially of two electrodes within a highly evacuated enclosure. One electrode, the cathode, is maintained at a high temperature and emits electrons from its surface. A potential difference of a few hundred volts is maintained between the cathode and the other electrode, known as the anode, with the anode at the higher potential.

Suppose a diode consists of a cylindrical cathode with a radius of 6.200 x10^-2 cm, mounted coaxially within a cylindrical anode with a radius of 0.5580 cm. The potential difference between the anode and cathode is 265 The potential difference between the anode and cathode is 265 V.  An electron leaves the surface of the cathode with zero initial speed (vinitial=0).  Find its speed vfinal  when it strikes the anode.

Express your answer numerically in meters per second.

Answer 1

The path of the electron going from the central cathode to the outer anode.

Since the diode is a cylinder, the symmetry implies that only radial motion needs to be considered for the electron, since any motion of the electron around the center will not change its potential energy.

The change in potential energy is .

, where is charge of electron and is the potential difference.

The law of conservation of energy is .

.

The kinetic energy is .

The initial velocity .

Substitute .

.

The final velocity .

Substitute , and .

.

The final speed when electron strikes the anode is .